A Different Method of Solving a Problem of IMO
International Journal of Systems Science and Applied Mathematics
Volume 5, Issue 1, March 2020, Pages: 1-3
Received: Jul. 30, 2019; Accepted: Sep. 10, 2019; Published: Apr. 1, 2020
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Author
Zhang Yue, Department of Physics, Hunan Normal University, Changsha, China
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Abstract
The IMO performs once a year, and has become an important activity in the field of mathematics. Because the problems in IMO are very difficult, and in general needs two days to finish the test of only six problems, therefore, it is significant to study how to solve and solve those IMO problems with various methods. With respect to question (a) of the problem of discussing, at first, using the so-called “exhaustive method” and the mathematical induction, the paper gets the conclusion of that if n is the integral multiple of 3, subtracting 1 from the nth power of 2 must be divisible by 7. Furthermore, it also proves by use of the disprove method that if n is not the integral multiple of 3, subtracting 1 from the nth power of 2 is impossible to be divisible by 7. The way of solving question (b) is similar to that of solving (a), in order to use the result of question (a) for the third step of the mathematical induction, the paper firstly consider the third power of that 1 added to (k+1)th power of 2 and applying the disprove method proves that it and hence that 1 added to the (k+1)th power of 2 are not divisible by 7, namely the question (b) is true.
Keywords
IMO, The Mathematical Induction, Algebraic Equation, Disprove Method
To cite this article
Zhang Yue, A Different Method of Solving a Problem of IMO, International Journal of Systems Science and Applied Mathematics. Vol. 5, No. 1, 2020, pp. 1-3. doi: 10.11648/j.ijssam.20200501.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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